Take three arbitrary points A, B, C on a circle and draw the respective Simson lines for some triangle DEF inscribed in the same circle. They build a triangle GHI similar to ABC. In particular this is independent of DEF, with respect to which we take the Simson lines.
This is a consequence of the property (discussed in SimsonProperty2.html ), according to which the angle of the simson lines from A and B is equal to half the angle <(AJB), which is equal to <(ACB).
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Three Simson Lines ![[0_0]](ThreeSimson_files/ThreeSimson_0_0_0.png)